“The World’s Greatest Tenor” – as Jonas Kaufmann, 47, is now regularly and not unjustifiably labelled – has had a rocky time of it since he last appeared in London in October 2015. As well as a run of respiratory infections, a burst blood vessel on his vocal cords – those damnably fragile strings of gristle on which a singer’s life depends – obliged him to make some embarrassing cancellations and endure months of silent convalescence. Many throats that suffer such a trauma never fully recover, and Kaufmann’s fans have all been praying that his full-time return to performance would not show signs of irrevocable decline.

So far, so good. Last month he earned glowing reviews for his Lohengrin at the Opéra Bastille in Paris, and now he is based for a couple of weeks at the Barbican Centre, where he is giving three concerts and a talk. The song recital which inaugurated this residency was simply superb.

Perhaps out of caution, it gave us short measure in terms of time (barely 70 minutes of singing, including a single brief encore in the form of Richard Strauss’s ebullient Nichts), but not of quality – here was a beautifully balanced programme of the greatest vocal music, interpreted with consummate artistry by both Kaufmann and his regular pianist Helmut Deutsch.

After a rather charmingly sheepish spoken apology for the music stand that would serve as a safety net if he forgot his words (he didn’t), Kaufmann opened with Schumann’s masterly Op. 35, a collection of a dozen songs set to poems by Justinus Kerner. At first, as if he was feeling his way forward, The World’s Greatest Tenor sounded tight and a little monochrome: Lust der Sturmnacht had no bloom to it, and with Deutsch carefully holding back to keep him free of pressure, no risks were taken.

But his marvellous solidity of technique – even legato, seamless tonal production and breath control, perfect tuning – was immediately evident, and in some sweetly whispered yet firmly projected pianissimi in Stirb, Lieb und Freud, the magic began to work its potent spell. Sehnsucht was rich in the colours that had previously been lacking; Stille Tränen floated through the song’s palpitating ardour; the final Alte Laute hung on a thread of desolate melancholy.

After the interval came five mélodies by Duparc. Here one was made aware of the tasteful elegance and rare intelligence that informs Kaufmann’s musicianship – he is never vulgar, never the popinjay playing to the gallery, and although he can be exquisitely refined, there is nothing affected about his style. The “luxe, calme, et volupté” of L’Invitation au Voyage and La Vie Antérieure were subtly but richly painted without wallowing in languor, while Le Manoir de Rosemonde became the most eerie of nightmare domains. Throughout Kaufmann’s French sounded excellent, but I wonder if he has a slight problem enunciating the acute é – Phidylé sounded more like Phidylee than Phidylay.

No such niggling reservations could be directed at the magnificent performance of Britten’s Seven Sonnets of Michelangelo, those exuberant hymns to the discovery of sexual love written in the wake of the composer’s initiation into physical passion. Deutsch became fully Kaufmann’s equal here: for the Duparc, he had evoked wisps of cloud and golden sunsets through some ravishing impressionistic pianism; for the Britten, he evoked trumpets, bells and drums, as Kaufmann celebrated and mused on the joys and woes of desire – never more alluringly than in the sinuously seductive Veggio co’ bei vostri occhi un dolce lume.

Such is Kaufmann’s relish of Britten’s vocal writing, is it too much to hope that he will one day sing Peter Grimes? Meanwhile, as well as his Siegmund in Act I of Die Walküre, Barbican audiences can look forward to Kaufmann’s appropriation of songs normally associated with women’s voices – Wagner’s Wesendonck Lieder and Strauss’s Four Last Songs. The World’s Greatest Tenor is not resting on his laurels.